Cherif Chekatt was killed on Thursday by police on a city street after he opened fire on officers.
Three people died following the shooting at the market and several more are seriously injured.
Interior Minister Christophe Castaner is due to attend the reopening.
Strasbourg's mayor Roland Ries said security would be tight: "We have restricted the number of entrances with checkpoints, body searches and bag searches. We have reduced [the number of entry points] for greater control, with a better distribution of police forces," he told French radio.
Strasbourg markets itself as the "capital of Christmas", and its festive market is a magnet for tourists, attracting two million visitors every year.
The city had been in lockdown after the attack while more than 700 police and soldiers hunted down the suspected gunman.
Chekatt, 29, had a string of criminal convictions in France and Germany and had become a radical Islamist in jail.
Interior Minister Christophe Castaner said three police officers had spotted a man matching Chekatt's description on rue du Lazaret, in the Neudorf area of Strasbourg at 21:00 local time (20:00 GMT).
As the police moved to stop him, the suspect turned round and opened fire. They fired back and "neutralised" the attacker, said Mr Castaner, who later went to the scene.
French President Emmanuel Macron thanked security forces in a tweet and vowed: "Our commitment against terrorism is total."
Hundreds of French police and security forces had been searching for Chekatt.
A large police operation had taken place in Neudorf earlier on Thursday, but ended apparently without results.
Five people have been arrested in connection with the attack. They include Cherif Chekatt's parents and two of his brothers.
Mr Ries said that finding Chekatt meant the worried people of his city would now be able to return to a normal life.
At about 20:00 local time (19:00 GMT), a man opened fire close to the famed Christmas market near place Kléber.
France's anti-terror prosecutor, Rémy Heitz, said the man had shouted "Allahu Akbar" ("God is greatest") as he opened fire.
The suspect was armed with a gun and a knife and escaped the area after jumping into a taxi, Mr Heitz said.
As he fled he came into contact with four soldiers, Mr Heitz said, and began firing at them. The soldiers fired back, apparently hitting him in the arm.
The attacker told the taxi driver he had killed 10 people, and also said he had been injured during a firefight with soldiers.
He ordered the taxi driver to drop him near the police station in Neudorf. When he got out of the vehicle, he fired at police officers before escaping.
Chekatt was born in Strasbourg and was already known to the security services.
He was on the "fiche S" watchlist of people who represent a potential threat to national security.
He had 27 convictions for crimes including robbery spanning France, Germany and Switzerland, and had spent considerable time in prison as a result.
Police were seeking him on Tuesday morning in connection with another case, but did not find him at home.
A search of his apartment in Neudorf revealed a grenade, a rifle, four knives - two of which were hunting knives - and ammunition.
The Islamic State group's self-styled news agency, Amaq, on Thursday said that Chekatt was "an Islamic State soldier" who had "carried out the operation in response to calls for targeting citizens of coalition countries" fighting its militants in Syria and Iraq.